Question

In a circle of radius 13 cm, AB is a chord and OP is perpendicular to AB. If OP = 5 cm, find length of AB​

Answer 1

Answer:

AB=24

Step-by-step explanation:

first you draw a circle, draw chord AB(not passing through the centre) and from the centre draw OP to AB such that OP⊥AB. Now join OA and OB. They become the two radii of the circle. now,

in triangle APO

OA^2- OP^2= AP^2                       (PYTHAGORUS THEOREM)

=>13^2-5^2=AP^2

=>169-25=AP^2

=>144=AP^2

=>AP=12

WE KNOW THAT A PERPENDICULAR FROM THE CENTRE OF A CIRCLE TO A CHORD BISECTS IT

=>AP=PB=12

=>AP+PB=12+12

=>AB=24

Answer 2

The length of chord AB is 24 cm.

Step-by-step explanation:

Given:

• In a circle of radius 13 cm.
• AB is a chord and OP is perpendicular to AB.
• If OP = 5 cm.

To find:

• Find length of AB.

Solution:

Concept \Theorem to be used:

• Perpendicular from centre of circle bisects chord.
• Apply Pythagoras theorem.

Step 1:

Apply Pythagoras theorem.

Draw the figure.

It is clear that, P is midpoint of the chord.

∆BOP is right triangle, right angle at P.

OP= 5 cm

OB= 13 cm

${OB}^{2} = {PB}^{2} + {OP}^{2}$

or

${PB}^{2} = {(13)}^{2} - {5}^{2}$

or

${PB}^{2} = 169 - 2 5$

or

$PB = \sqrt{144}$

or

$\bf PB = 12 \: cm$

Step 2:

Find the length of chord AB.

As, P is midpoint of AB.

So,

$AB = 2PB$

or

$AB= 2 \times 12$

or

$\bf AB = 24 \: cm$

Thus,

Length of chord AB is 24 cm.

Learn more:

1) distance of a chord AB of a circle from the centre is 12cm and length of the chord AB is 10cm. find the diameter of the ...

https://brainly.in/question/6653415

2)in a circle of radius 13 cm is drawn at a distance of 12 CM of the centre find the length of the chord

https://brainly.in/question/6856048

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